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Diffusion on the Scaling Limit of the Critical Percolation Cluster in the Diamond Hierarchical Lattice

Abstract:

We construct critical percolation clusters on the diamond hierarchical lattice and show that the scaling limit is a graph directed random recursive fractal. A Dirichlet form can be constructed on the limit set and we consider the properties of the associated Laplace operator and diffusion process. In particular we contrast and compare the behaviour of the high frequency asymptotics of the spectrum and the short time behaviour of the on-diagonal heat kernel for the percolation clusters and for...

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Publication status:
Published

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Publisher copy:
10.1007/s00220-009-0981-3

Authors


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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
Journal:
COMMUNICATIONS IN MATHEMATICAL PHYSICS
Volume:
295
Issue:
1
Pages:
29-69
Publication date:
2010-04-01
DOI:
EISSN:
1432-0916
ISSN:
0010-3616
Source identifiers:
48968
Language:
English
Pubs id:
pubs:48968
UUID:
uuid:b6374cd3-aec5-47a0-8c0a-24d9c93d3453
Local pid:
pubs:48968
Deposit date:
2012-12-19

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